The present invention relates to an interference canceller using an adaptive filter for approximating the transfer function of the propagation path of interfering signals.
Adaptive noise cancelling is described in a paper "Adaptive Noise Cancelling: Principles and Applications", Bernard Widrow et al., Proceedings of The IEEE, Vol. 63. No. 12, December 1975, pages 1692 to 1716. The paper describes an LMS (least means square) adaptive noise canceller in which a signal s.sub.k is transmitted over a channel and received by a first sensor that also receives a noise n'.sub.k uncorrelated with the signal, where k represents the instant of discrete time. The combined signal and noise s.sub.k +n'.sub.k form the primary input to the canceller. A second sensor receives a noise n.sub.k uncorrelated with the signal but correlated in some unknown way with the noise n'.sub.k. This sensor provides the reference input to the canceller. The noise n.sub.k is processed by an adaptive filter to produce an output n.sub.k that is a replica of noise n'.sub.k. This filter output is subtracted from the primary input s.sub.k +n'.sub.k to produce the system output d.sub.k =s.sub.k +n'.sub.k -n.sub.k. The system output d.sub.k is scaled by a factor 2.alpha. by a multiplier, (where .alpha. is a constant called `stepsize`). This adaptive filter has tap weight coefficients c.sub.0 through c.sub.N-1 that are controlled in response to the multiplier output to approximate the impulse response of the transmission channel of noise n'.sub.k to the primary input of the canceller. All tap coefficients of the filter are given in matrix form by the following Equation: EQU c.sub.k =c.sub.k-1 +2.alpha..multidot.d.sub.k .multidot.n.sub.k-1( 1)
where, c.sub.k and n.sub.k are represented by: EQU c.sub.k =[c.sub.0 .multidot.c.sub.1 . . . c.sub.N-1 ].sup.T( 2) EQU n.sub.k =[n.sub.0 .multidot.n.sub.1 . . . n.sub.N-1 ].sup.T( 3).
The second term of Equation (1) is called the tap-weight trimming value with which the tap weights are updated at periodic intervals.
To achieve tap-weight convergence stability, a paper titled "Learning Identification Method: LIM", IEEE Transactions On Automatic Control, Vol. 12, No. 3, 1967, pages 282-287, describes a method in which the tap weights are controlled according to the following Equation: EQU c.sub.k .perspectiveto.c.sub.k-1 +(2.mu./N.sigma..sub.n.sup.2).multidot.d.sub.k .multidot.n.sub.k-1( 4)
where .mu. is the stepsize of the LIM algorithm and .sigma..sub.n.sup.2 represents an average power of the primary input signal to the adaptive filter.
Another prior art is the adaptive line enhancer (ALE) in which the signal s.sub.k is a wideband signal and the noise n'.sub.k is a periodic signal. These signals are combined to form the primary input to the ALE. The reference input n.sub.k to the ALE is a delayed version of the primary signal. By tap-weight convergence, interference between the wideband and periodic signals is cancelled.
One shortcoming of the prior art techniques is that, during a tap-weight convergence process, signal s.sub.k interferes the residual noise n'.sub.k -n.sub.k which is the only necessary component for tap-weight adaptation. The degree of interference depends on the relationship between the residual noise and signal s.sub.k and on the stepsize value. The tap-weight trimming value varies as a function of the signal-to-noise ratio (SNR) of signal s.sub.k, the spectrum of signal s.sub.k and the stepsize. For large values of SNR, a relation .vertline.s.sub.k .vertline.&gt;.vertline.n'.sub.k -n.sub.k .vertline. holds and the trimming value is severely interfered with signal s.sub.k. If signal s.sub.k contains an increasing proportion of high frequency components, the relation .vertline.s.sub.k .vertline.&gt;.vertline.n'.sub.k -n.sub.k .vertline. holds instantaneously with a higher likelihood of occurrences even if the SNR is of a small value. Therefore, at some peak points, the signal s.sub.k may exceed the residual noise, resulting in a low probability with which valid tap-weight trimming values occur. By taking the amplitude distribution of signal s.sub.k into account, the stepsize must be chosen at a value that is sufficiently small to prevent tap weight divergence. Thus, the tendency is toward choosing the stepsize at an unnecessarily small value with an attendant low convergence speed or at a value which is relatively large but slightly smaller than is required to prevent divergence with an attendant high probability of incorrect tap weight adjustment.
Following the convergence process, the system output d.sub.k is rendered equal to the residual noise n'.sub.k -n.sub.k is signal s.sub.k is nonexistent, and hence the tap-weight trimming values are zero. Whereas, if signal s.sub.k is present, the system output d.sub.k is nonzero even if n'.sub.k -n.sub.k and hence the coefficient trimming factor is nonzero. Another shortcoming of the prior art is that, if signal s.sub.k is present, the tap weights are updated with nonzero system output d.sub.k, and a residual noise proportional to the stepsize is generated.